Question

GIẢI PHƯƠNG TRÌNH\(\frac{x}{2x-6}+\frac{x}{2x+2}-\frac{2x}{\left(x+1\right)\left(x-3\right)}=0\)

Answer 1

\(\frac{x}{2\left(x-3\right)}+\frac{x}{2\left(x+1\right)}-\frac{2x}{\left(x+1\right)\left(x+3\right)}=0\)

\(\frac{x\left(x+1\right)}{2\left(x-3\right)\left(x+1\right)}+\frac{x\left(x-3\right)}{2\left(x-3\right)\left(x+1\right)}-\frac{2.2x}{2\left(x-3\right)\left(x+1\right)}=0\)

\(\frac{x^2+x}{2\left(x-3\right)\left(x+1\right)}+\frac{x^2-3x}{2\left(x-3\right)\left(x+1\right)}-\frac{4x}{2\left(x-3\right)\left(x+1\right)}=0\)

\(\frac{x^2+x+x^2-3x-4x}{2\left(x-3\right)\left(x+1\right)}=0\)

\(\frac{2x^2-6x}{2\left(x-3\right)\left(x+1\right)}=0\)

=>\(2x^2-6x=0\)

\(2x\left(x-3\right)=0\)

=>\(x=0\)

\(x=3\)